Question

You have been assigned to assess the performance a Fund Manager: Cepat Kaya for a contract for next 5 years. Based on historical data you found that 70% of times this fund manager able to exceed your target. Do the following things: 

a. Calculate the probability that for the next contract, this fund manager can beat your target at least 3 annual reviews. Will you extend the contract? Why 

b. You obtain new information that the chief investment officer of Cepat Kaya will be replaced by a person that less qualified hence you think that the probability of beating the target in any given year should drop to 0.4. Recalculate the answer in point a. Will you extend the contract? Why?

Answer 1

(a) To calculate the probability that the fund manager can beat the target at least 3 annual reviews, we need to consider the binomial distribution. Let's assume the next 5 years are independent and the probability of beating the target in any given year is 0.7.

The probability of beating the target in exactly k out of n years is given by the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

• n is the total number of years (5)

• k is the number of years the fund manager beats the target (3, 4, or 5)

• p is the probability of beating the target in any given year (0.7)

To calculate the probability of beating the target at least 3 times, we sum the probabilities for k = 3, 4, and 5:

P(X >= 3) = P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial probability formula, you can calculate these probabilities and add them up.

If the probability of beating the target at least 3 times is high enough (e.g., above a predetermined threshold), it may indicate a good performance, and you may consider extending the contract. The decision ultimately depends on the specific threshold or criteria set by the contract.

(b) If you obtain new information that the probability of beating the target in any given year should drop to 0.4 due to the replacement of the chief investment officer, you would need to recalculate the probabilities in point (a) using the updated probability (p = 0.4).

Following the same approach as in (a), you can calculate the probabilities for beating the target at least 3 times with the updated probability and compare them to your threshold. If the probabilities are significantly lower, it may indicate a decrease in performance, and you may reconsider extending the contract.